The Chvátal-Erdős condition and 2-factors with a specified number of components

• Autorzy: Guantao Chen , Ronald J. Gould , Ken-ichi Kawarabayashi , Katsuhiro Ota , Akira Saito , Ingo Schiermeyer
• Języki publikacji: EN

Abstrakty

EN

Let G be a 2-connected graph of order n satisfying α(G) = a ≤ κ(G), where α(G) and κ(G) are the independence number and the connectivity of G, respectively, and let r(m,n) denote the Ramsey number. The well-known Chvátal-Erdös Theorem states that G has a hamiltonian cycle. In this paper, we extend this theorem, and prove that G has a 2-factor with a specified number of components if n is sufficiently large. More precisely, we prove that (1) if n ≥ k·r(a+4, a+1), then G has a 2-factor with k components, and (2) if n ≥ r(2a+3, a+1)+3(k-1), then G has a 2-factor with k components such that all components but one have order three.

Słowa kluczowe

EN

Chvátal-Erdös condition; 2-factor; hamiltonian cycle; Ramsey number

Kategorie tematyczne

• 05C45: Eulerian and Hamiltonian graphs
• 05C38: Paths and cycles
• 05C69: Dominating sets, independent sets, cliques
• 05C40: Connectivity

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2007
• Tom: 27
• Numer: 3
• Strony: 401-407

Daty

wydano

2007

otrzymano

2006-03-01

poprawiono

2007-07-23

zaakceptowano

2007-07-23

Twórcy

autor

Guantao Chen

• Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA

autor

Ronald J. Gould

• Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA

autor

Ken-ichi Kawarabayashi

• National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-Ku, Tokyo 101-8430, Japan

autor

Katsuhiro Ota

• Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Kohoku-Ku, Yokohama 223-8522, Japan

autor

Akira Saito

• Department of Computer Science, Nihon University, Sakurajosui 3-25-40, Setagaya-Ku, Tokyo 156-8550, Japan

autor

Ingo Schiermeyer

• Institut für Diskrete Mathematik und Algebra, Technische Universität, Bergakademie Freiberg, D-09596 Freiberg, Germany

Bibliografia

• [1] A. Bondy, A remark on two sufficient conditions for Hamilton cycles, Discrete Math. 22 (1978) 191-194, doi: 10.1016/0012-365X(78)90124-3.
• [2] S. Brandt, G. Chen, R. Faudree, R. Gould and L. Lesniak, Degree conditions for 2-factors, J. Graph Theory 24 (1997) 165-173, doi: 10.1002/(SICI)1097-0118(199702)24:2<165::AID-JGT4>3.0.CO;2-O
• [3] G. Chartrand and L. Lesniak, Graphs & Digraphs (3rd ed.) (Wadsworth & Brooks/Cole, Monterey, CA, 1996).
• [4] V. Chvátal and P. Erdös, A note on hamiltonian circuits, Discrete Math. 2 (1972) 111-113, doi: 10.1016/0012-365X(72)90079-9.
• [5] Y. Egawa, personal communication.
• [6] H. Enomoto, On the existence of disjoint cycles in a graph, Combinatorica 18 (1998) 487-492, doi: 10.1007/s004930050034.
• [7] A. Kaneko and K. Yoshimoto, A 2-factor with two components of a graph satisfying the Chvátal-Erdös condition, J. Graph Theory 43 (2003) 269-279, doi: 10.1002/jgt.10119.
• [8] O. Ore, Note on Hamilton circuits, Amer. Math. Monthly 67 (1960) 55, doi: 10.2307/2308928.

Identyfikatory

DOI

10.7151/dmgt.1370